The Mathematisation of Nature

The idea that nature was fundamentally 'mathematical' was current in the 17th Century, and came to play a key role in the work of Newton and in later science, but in the early phase of the scientific revolution, the mechanical philosophy stood in its way.

The science of mechanics was the expression in early 17th Century science of the mathematising spirit, the view that phenomena were describable in exact mathematical terms. It had an ancient source in Pythagoras. The new astronomy was an early field of application.

(See Westfall p.120.)

Spinoza

Closely related is the pure rationalism developed by Benedictus de Spinoza (1632-77).

Reason gives us a portal onto the fundamental character of the world: the relations between ideas, as grasped by the mind, reflect the relations between features of reality. (For Spinoza in fact these two things perhaps amount to one and the same.)

All truths are necessary truths, like the truths of geometry, and like them things we can be certain about with the application of thought.

Substance is understood (as in Descrates) as that which depends on nothing else. We can be certain, through the ontological proof, that God exists, and consequently that there is just one substance. Where Descartes spoke of two types of substance, material and mental (there was just the one material substance and a pluraity of mental substances - minds), Spinoza maintained there can only be one. So there is an identity between God and mentality and materiality. " God is immanent in the world, and individual things are themselves modes or modifications of God: the one reality is 'God or Nature'." (Blackburn's Dictionary entry for 'Spinoza'.) Extension (materiality) and thought are two different ways in which reality - God - may be conceived. Science is to be understood as the attempt to understand how everything that happens happens necessarily, and everything that exists does so necessarily.

In spite of the necessity which rules reality, human agency is real nonetheless. But excercising freedom is a matter of one's thoughts coming into line with what is necesarily happening.

An authoritative discussion of key aspects of Spinoza's philosophy is offered by Susan James in her Passion and Action, Oxford, 1997, Clarendon, Ch 6.